Current approaches to dose choice

• A few doses are explored in phase I/II trials, one is chosen for phase III and licensure.

Example of BioNTech/Pfizer COVID Vaccine

Claim: Knowing in more detail how dose impacts host response following vaccination might help optimize vaccines.

Motivation

• Most vaccines aim to induce strong antibody responses.
• For a future norovirus vaccine, it is important to understand how dose impacts antibody responses.
• It is also informative to understand if there are differences in antibody kinetics following infection vs. vaccination.

Study design

Models

Exponential decay model: \[ y_1(t) = \frac{p_1}{1+e^{(-g_1*(t-k_1))}}e^{-d_1*t} \]

Power-law decay model: \[ y_2(t) = \frac{p_2}{1+e^{(-g_2*((t+1)-k_2))}}(t+1)^{-d_2} \]

Vaccination antibody time-series

Hierarchical/mixed-effects modeling framework

Vaccination antibody time-series

Vaccination antibody time-series

Vaccination antibody early response

Vaccination antibody durability

Comments

• We have applied similar statistical analyses to influenza vaccines.
• We have also used a similar approach to explore the impact of dose following infection.

Objectives

For this project, the goals were to:

• Develop a conceptual framework combining data with mechanistic models to investigate the impact of dose on infection dynamics.
• Link the models to vaccine outcomes (protection and morbidity).
• Illustrate how to use this framework to predict outcomes for a large range of doses.

We focused on viral infections as a stand-in for live attenuated vaccines.

Influenza (vaccine)

Handel et al 2018 PLoS Comp Bio

Modeling dose and immune response

Modeling dose and immune response

\[ \begin{aligned} \textrm{Uninfected cells} \qquad \dot{U} & = - bUV \\ \textrm{Infected cells} \qquad \dot{I} & = bUV - d_I I \\ \textrm{Dead cells} \qquad \dot{D} & = d_I I \\ \textrm{Virus} \qquad \dot{V} & = \frac{pI}{1+s_F F} - (d_V V + k^{'}_{A}A + b^{'} U)V\\ \textrm{Innate response} \qquad \dot{F} & = p_F - d_F F + \frac{g_F (F_{max} - F)V}{V+h_V} \\ \textrm{B cells} \qquad \dot{B} & = \frac{F V}{FV+h_F} g_B B \\ \textrm{Antibodies} \qquad \dot{A} & = r_A B - d_A A - k_{A}AV \\ \end{aligned} \]

Modeling dose and immune response

Mapping antibodies to protection

We want to know protection. We can map antibodies to it. We use this relation: \(P=1−1/(1+e^{k_1(log(A)−k_2)})\)

Coudeville et al 2010 BMC Med Res Meth

Mapping innate response to morbidity

We want to know morbidity (side effects/symptoms). We can map the innate response to it. \[ M = \int \frac{aF^c}{b+F^c} \]

Hayden et al 1998 JCI

Dose for influenza vaccine

Conceptual model suggests that protection (and morbidity) could be peaked.

Motivation

• For a future norovirus vaccine, explore what vaccination strategies have the most impact.

Steele et al 2016 Epidemics

Methods

• Compartmental, SIR type ODE model.

• Model fit to norovirus incidence data.

Results

R packages to make modeling easier I

For teaching (stable):

• Dynamical Systems Approach to Immune Response Modeling

• Dynamical Systems Approach to Infectious Disease Epidemiology (Ecology/Evolution)

R packages to make modeling easier II

For research (WIP):

• flowdiagramr
• modelbuilder

Online modeling/analysis courses

• Simmulation Modeling in Immunology
  • See also Handel et al 2020 Nat Rev Imm
• Modern Applied Data Analysis
• Infectious Disease Epidemiology (Ecology)(Evolution) - A model-based approach
• Some more projects here